Algebra Seminar: Representations and spin representations of the symmetric group which have the same p-modular reductions

Abstract: When do two ordinary irreducible representations of a group have the same p-modular reduction? I will explain how this question can equivalently be understood in terms of character values. I will then present an (almost complete) answer to this question for the double cover of the symmetric group. Representations of the double cover which are not representations of the symmetric group itself are called spin representations, and I will focus on the case of when a spin and non-spin representation have the same p-modular reduction. I will give a necessary and sufficient condition for this, and explain some of the techniques used in the proof. In particular I will describe a combination of induction and restriction functors which has the effect of swapping adjacent runners in an abacus display for the labelling partition of a representation. This is based on joint work with Matt Fayers.

Join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.